Burke and Amukamara scored all of the Sun Devils' points in an 8-2 run to go ahead 91-85 with 1:14 left and they finished with five of Arizona State's final six points.
Oregon closed to within 94-92 on Danielle Love's free throws with 15 seconds left. The Ducks sent Elisha Davis to the line where she made the first and missed the second. Amukamara grabbed the offensive rebound and made two more free throws to put the Sun Devils up 97-92.
Katie Hempen added 16 points, Elisha Davis scored 11 and Deja Mann had 10 assists for Arizona State (19-3, 8-2) which stays alone in second in the Pac-12.
Freshman Chrishae Rowe scored 39 points to lead the Ducks (12-9, 3-7) but committed eight turnovers.
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